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Turkish Journal of Mathematics

DOI

10.55730/1300-0098.3130

Abstract

Let $J_\nu(z)$ denote the Bessel function of the first kind of order $\nu.$ In this paper, our aim is to determine the radii of starlikeness and convexity for three kind of normalization of the function $N_\nu(z)=az^{2}J_{\nu }^{\prime \prime }(z)+bzJ_{\nu }^{\prime }(z)+cJ_{\nu }(z)$ in the case where zeros are all real except for a single pair, which are conjugate purely imaginary. The key tools in the proof of our main results are the Mittag-Leffler expansion for function $N_\nu(z)$ and properties of real and complex zeros of it.

First Page

894

Last Page

911

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